Energetic and Spectroscopic Properties of Astrophysically Relevant MgC4H Radicals Using High-Level Ab Initio Calculations

Considering the importance of magnesium-bearing hydrocarbon molecules (MgCnH; n = 2, 4, and 6) in the carbon-rich circumstellar envelopes (e.g., IRC+10216), a total of 28 constitutional isomers of MgC4H have been theoretically investigated using density functional theory (DFT) and coupled-cluster methods. The zero-point vibrational energy corrected relative energies at the ROCCSD(T)/cc-pCVTZ level of theory reveal that the linear isomer, 1-magnesapent-2,4-diyn-1-yl (1, 2Σ+), is the global minimum geometry on the MgC4H potential energy surface. The latter has been detected both in the laboratory and in the evolved carbon star, IRC+10216. The calculated spectroscopic data for 1 match well with the experimental observations (error ∼ 0.78%) which validates our theoretical methodology. Plausible isomerization processes happening among different isomers are examined using DFT and coupled-cluster methods. CASPT2 calculations have been performed for a few isomers exhibiting multireference characteristics. The second most stable isomer, 1-ethynyl-1λ3-magnesacycloprop-2-ene-2,3-diyl (2, 2A1, μ = 2.54 D), is 146 kJ mol–1 higher in energy than 1 and possibly the next promising candidate to be detected in the laboratory or in the interstellar medium in future.


INTRODUCTION
−9 In 1987, the first metal-containing molecules were detected in the ISM by Cernicharo et al. in the evolving carbon star IRC+10216, which is ∼310 light years away from earth. 10 Later in 2010, Mauron and Huggins detected a few more alkali and transition metal atoms such as Na, K, Ca, Fe, and Cr, along with some of their ionic forms in the gas-phase region of IRC+10216. 11−24 To date, magnesium is the only metal found in IRC+10216 having molecules containing more than three atoms.
Most of the metal-bearing species in the ISM have been detected by comparing the radioastronomical data to the observed rotational spectra in the laboratory.However, the synthesis, characterization, and eventual identification of such transient species in the laboratory are not a very easy task.−31 Moreover, the spectroscopic detection and identification of these molecules can be challenging due to the presence of the metal atom having many closely spaced electronic states with different spin multiplicities.
Magnesium-containing molecules (MgCN and MgNC) were first discovered in IRC+10216 earlier in 1995 by Ziurys et al. 15 Later, in 2017, magnesium acetylides and cyanides were detected in the cold region of the carbon-rich stars IRC+10216 and CRL 2688. 32−39  Highberger et al. in  2001 and 2003 identified MgNC in two protoplanetary nebulae, CRL 2688 and CRL 618. 40,41It was believed that the isoelectronic structures of MgNC/MgCN such as MgC 2 H might be present in the ISM, and the pure rotational spectra of MgC 2 H were recorded by Ziurys and co-workers in 1995. 42,43ater in 2014, MgC 2 H was tentatively identified in IRC+10216 by Agundez et al. 44 Recently, in 2019, Cernicharo et al. discovered another two important magnesium-containing species MgC 3 N and MgC 4 H in IRC+10216 along with the confirmation of the presence of MgC 2 H. 45 In 2021, Pardo et al. identified MgC 5 N and its isoelectronic molecule MgC 6 H (1magnesahept-2,4,6-triyn-1-yl) in IRC+10216. 46Recently, in 2023, HMgC 3 N, NaC 3 N, MgC 4 H + , MgC 6 H + , MgC 3 N + , and MgC 5 N + have been detected in IRC+10216. 47,48aier and co-workers experimentally recorded the electronic transitions of MgC 2n H (n = 1−3) in the gas phase using a mass selective, resonant, two-color two-photon ionization technique and a laser ablation source. 49,50In 2010, Forthomme et al. recorded the high-resolution spectra of the electronic transition of MgC 4 H using laser-induced fluorescence. 51Guo et al. have theoretically calculated the electronic spectra of linear MgC 2n H (n = 1−5) using the multireference secondorder perturbation theory (CASPT2). 52Till date, only the linear MgC 4 H isomer (1-magnesapent-2,4-diyn-1-yl; 1) with magnesium at one end has been detected in the laboratory and in IRC+10216. 45,49Since the synthesis and identification of other low-lying isomers of MgC 4 H remain as an open challenge, we have explored the potential energy surface (PES) of MgC 4 H isomers to determine their structural isomers, thermodynamic and kinetic stabilities, and also the spectroscopic properties in their doublet and quartet electronic states.
In this study, 28 stationary points of MgC 4 H have been investigated using high-level quantum chemical calculations.In pursuit of improved accuracy for relative energies and spectroscopic properties, coupled-cluster (CC) methods were adopted.The geometry optimizations and frequency calcu-lations were executed for the first seven low-lying isomers in their doublet and quartet electronic states.Similar to isomer 1, we have identified another two possible linear isomers, 3magnesapent-1,4-diyn-1-yl (3) and 1-magnesapent-2,4-diyn-5yl (7), where the magnesium atom is present at the center and in between the terminal carbon and hydrogen atoms, respectively.Though higher in energy, isomer 7 has a large dipole moment (μ = 5.53 D) among all linear isomers.The lowest-energy cyclic isomer, 1-ethynyl-1λ 3 -magnesacycloprop-2-ene-2,3-diyl (2, 2 A 1 ), is 146 kJ mol −1 higher in energy compared to linear isomer 1.However, this isomer (2) has not been detected either in the laboratory or in ISM to date, to the best of our knowledge.
The energetics, electronic structures, Wiberg Bond Indices (WBIs), topological analysis, kinetic stability, and most important spectroscopic properties have been analyzed in this study.In addition, thermodynamically favorable rearrangement schemes have been postulated for the formation of lowlying MgC 4 H isomers from its higher-energy isomers.These rearrangement pathways may aid experimental chemists in detecting unknown low-lying isomers in the laboratory.

COMPUTATIONAL METHODOLOGY
All stationary points in the PES of MgC 4 H have been first identified using density functional theory (DFT) at the UωB97XD 53 /6-311++G(2d,2p) 54,55 level of theory.Among the 28 isomers considered for the present study, 15 are found to be minima (with no imaginary frequencies), 7 are found to be transition states (with one imaginary frequency), and the rest are higher-order saddle points with more than one imaginary frequency.ωB97XD hybrid functional was chosen on purpose as it incorporates empirical dispersion corrections. 56Since the ground electronic states of various MgC 4 H

The Journal of Physical Chemistry A
isomers are in the doublet spin state, both restricted and unrestricted Hartree−Fock (UHF) wave functions are used in all calculations.For the first seven low-lying isomers, DFT calculations have also been carried out with the Perdew− Burke−Ernzerhof (PBE0) 57 functional at both ROPBE0-D3/ def-TZVP and UPBE0-D3/def-TZVP levels, and full geometry optimization and frequency calculations have been carried out using the CC method at the ROCCSD(T) 58−60 /cc-pCVTZ 61−63 and UCCSD(T)/cc-pCVTZ levels in both doublet and quartet ground electronic states.The singlepoint energy calculation for low-lying isomers has been performed at the CCSD(T)-F12 64 /cc-pVTZ-F12 65 level of theory using ORCA software. 66Considering the high multireference character (high T 1 diagnostic value) of some lowlying isomers, complete-active-space second-order perturbation theory (CASPT2) 67 calculations have been performed using ORCA software.The entire π-electron system and all valence and unpaired electrons of the Mg atom are included using (11,11) active space, and the cc-pVTZ basis set has been used for this calculation.Furthermore, to understand the nature of bonding in MgC 4 H isomers, atoms in molecule analysis was performed for these isomers using the multifunctional wave function analyzer program, Multiwfn. 68hermodynamically favorable pathways for the formation of low-lying isomers from the higher-energy isomers have been calculated at the UB3LYP 69,70 /6-311++G(2d,2p) level of theory.The appropriate transition states are also calculated using the same level of theory.The isomerization pathways have been confirmed through intrinsic reaction coordinate (IRC) 71,72 calculations at the same level.Furthermore, to refine the relative energies, the single-point energy calculation for all isomers and transition states has been carried out at the CCSD(T)/cc-pVTZ level of theory.To evaluate the multireference character, T 1 diagnostic values 73 have been calculated at the UCCSD/6-311++G(2d,2p)//UωB97XD/6-311++G-(2d,2p) level of theory.Some of the isomers possess a strong multireference character (T 1 diagnostic value >0.02).To understand better the electronic structural information for these isomers, a higher-level CASPT2 calculation have been performed.In addition, to determine the kinetic stability, ab initio molecular dynamics (AIMD) simulations have been performed at the UωB97XD/6-311++G(2d,2p) level of theory using the atom-centered density matrix propagation 74 method for the low-lying isomers listed in ESI (Figure S3).All DFT calculations and AIMD simulations are carried out using Gaussian suite of programs. 75All CC calculations have been performed out using the CFOUR program package. 76

RESULTS AND DISCUSSION
The optimized geometries of the doublet electronic state of the first seven low-lying isomers of MgC 4 H along with the point group symmetries and permanent dipole moments are shown in Figure 1.The zero-point vibrational energy (ZPVE) corrected relative energies (ΔE 0 ; in kJ mol −1 ) obtained at various levels of theories for these low-lying isomers have been presented in Table 1.The spectroscopic parameters, e.g., inertial axis dipole moments along with their Cartesian components, rotational constants, and the centrifugal distortion constants in their doublet electronic states, have been listed in Table 2.The color-filled ELF plot at the (3, −1) critical point of the first seven low-lying isomers is shown in Figure 2. Thermodynamically favorable rearrangement scheme for the isomerization of low-lying isomers and the correspond-  represents the relative energies calculated from CASPT2 using the (11,11) active space and the cc-pVTZ basis set as implemented in the ORCA software.

The Journal of Physical Chemistry A
ing PES are depicted in Figure 3.All other high-energy isomers and transition states are shown in Figures 4 and 5, respectively.The optimized geometries of the first seven low-lying isomers of MgC 4 H isomers in their corresponding quartet electronic states are shown in ESI.This section is organized into the following subsections: The energetics and the electronic structures of all isomers are discussed in Section 3.1.WBIs, topological analyses, spectroscopic properties, and thermodynamically favorable rearrangement schemes have been conferred in Sections 3.2− 3.5.In Section 3.6, all other high-energy isomers and transition states have been discussed.
3.1.Energetics.3.1.1.Linear and Branched Isomers.The doublet electronic state ( 2 Σ + ) of 1-magnesapent-2,4-diyn-1-yl (1) has been found to be the most stable isomer among all isomers of MgC 4 H considered in the present study.In 2019, isomer 1 was detected in the carbon star IRC+10216 45 by Cernicharo et al.The optimized geometry of 1 at the ROCCSD(T)/cc-pCVTZ level shows a long chain isomer with two acetylenic moieties and a magnesium atom present at the terminal position.The ground electronic state of neutral 1 is 2 Σ + (C ∞v symmetry) with electronic configuration (1− 6σ) 2 (1π) 4 (7−12σ) 2 (2π) 4 (3π) 4 (13σ) 1 .The spin density distribution calculation of 1 at the RCCSD(T)/cc-pCVTZ level of theory indicates that the unpaired electron is primarily located at the magnesium atom, whereas the electron cloud has certain extension toward the neighboring C 1 atom.The C−C bond distances of C 1 −C 2 and C 3 −C 4 are 1.233 and 1.214 Å (as shown in Figure 1), indicating triple bond character.Again, the C 2 −C 3 (1.376Å) bond shows partial double bond character representing the electronic delocalization, thereby justifying the high dipole moment of 2.09 D. Furthermore, the natural atomic charges of 1 depicted that the Mg−C 1 bond is ionic in character.Our calculated bond angles and bond distances are in excellent agreement with the bond lengths and angles obtained earlier within various (B3LYP/aug-cc-pVTZ, C C S D ( T ) / a u g -c c -p V T Z , C A S P T 2 / 6 -3 1 G * ) a pproaches. 23,45,50,52The quartet electronic state ( 4 Σ + ) of 1 (389 kJ mol −1 higher in energy than the doublet 1) is also a minimum energy structure in the MgC 4 H quartet PES.The quartet electronic structure of this isomer is relatively less polar (0.5 D) than the doublet one; however, the overall molecular symmetry remains the same (C ∞v ).The optimized geometry at  The experimental rotational constant value (B 0 ) for isomer 1 is 1381.512MHz 45 discovered in IRC+10216.The calculated percentage of error from the experimental to theoretical rotational constant value is ≃0.78%.b represents the spectroscopic parameters calculated from CASPT2 using the (11,11) active space and the cc-pVTZ basis set.3-Magnesapent-1,4-diyn-1-yl (3) and 1-magnesapent-2,4diyn-5-yl ( 7) have similar skeletal structures (linear structure) with 1; the only difference is in the position of magnesium atom.The magnesium atom is in the middle position in the case of 3 but at the terminal position in both isomers 1 and 7 which differs only in the position of the hydrogen atom.Isomer 3 is 178 kJ mol −1 higher in energy than 1.The latter contains two acetylenic moieties with bond distances of 1.238 Å (C 1 − C 2 ) and 1.224 Å (C 3 −C 4 ) (Figure 1).The hydrogen atom is attached with one of the terminal carbon atom (C 4 ).The ground doublet electronic state of neutral 3 is 2 Σ + (C ∞v symmetry) with the electronic configuration (1− 6σ) 2 (1π) 4 (7−12σ) 2 (2π) 4 (3π) 4 (13σ) 1 .The spin density distribution calculation at the ROCCSD(T)/cc-pCVTZ level of theory indicates that the unpaired electron primarily resides at the terminal carbon atom (C 1 ) having no attached hydrogen.As no such ionic bonds or delocalized bonds are present in this isomer, the total dipole moment is little low (1.30D).The quartet electronic state of 3 is 4 Σ + (474 kJ mol −1 above the doublet of 3).The overall symmetry of this isomer remains the same for both electronic states (C ∞v ).Similar to isomer 1, the quartet state geometry is much less polar (μ = 0.14 D) compared to the doublet one (μ = 1.30D).The elongated C 1 −C 2 bond (0.133 Å higher than the doublet 3) may be due to a C−C partial double bond.However, the equilibrium rotational constant value (B e ) of doublet 3 is ∼37 MHz higher than that of the quartet electronic state.

The Journal of Physical Chemistry A
(1.335 Å) shows double bond characteristics, which implies the delocalization of electrons through C 1 to C 4 .The total dipole moment of 7 is 5.52 D, which indicates that this isomer can be easily detected through rotational spectroscopy.Furthermore, the quartet ( 4 Σ + ) electronic state of 7 is 288 kJ mol −1 above that of its doublet ( 2 Σ + ) at the ROCCSD(T)/cc-pCVTZ level of theory.The equilibrium rotational constant ( 2 Σ + 1357.42MHz and 4 Σ + 1334.93MHz), bond distances, and bond angles of this isomer in both the electronic states predict that it is a linear molecule with C ∞v molecular symmetry.
Another long chain isomer with C s molecular symmetry is 5magnesapent-1-ene-3-yn-1-yl (5; 204 kJ mol −1 higher energy than 1).The only difference in the skeletal structure of 5 from 1 is the position of the hydrogen atom; instead of the terminal carbon atom, the hydrogen atom is attached with the neighboring carbon of the terminal carbon.As the hydrogen atom is attached to the second carbon atom, the overall geometry is no longer linear, as shown in Figure 1.The ground electronic state of 5 is 2 A′ with the electronic configuration (1−7A′) 2 (1A″) 2 (8−13A′) 2 (2A″) 2 (14−15A′) 2 (3A″) 2 (16A′) 1 .The spin density distribution calculation at the ROCCSD(T)/ cc-pCVTZ level of theory predicts that the unpaired electron is primarily located at the terminal magnesium atom.The optimized geometry at the ROCCSD(T)/cc-pCVTZ level of theory shows that C 1 −C 2 (1.309 Å), C 2 −C 3 (1.443Å), and C 3 −C 4 (1.227Å) exhibit double bond, partial double bond, and triple bond characteristics, respectively.Moreover, the terminal carbon atom acts as a carbene carbon.Furthermore, C 2 C 3 C 4 (176.43°)and C 3 C 4 Mg (178.35°)bond angles are shorter than 180°, and C 1 C 2 C 3 (101.64°) is shorter than the ideal sp 2 bond angle.The quartet electronic state of 5 is 4 A′, 193 kJ mol −1 higher in energy than the corresponding doublet electronic state.
The point group of isomer 4 is C s , and the ground electronic state is 2 A′ with the electronic configuration (1− 6A′) 2 (1A″) 2 (7−12A′) 2 (2A″) 2 (13−15A′) 2 (3A″) 2 (16A′) 1 .This molecule is 198 kJ mol −1 higher in energy than doublet 1.The spin density distribution calculation at the ROCCSD(T)/ cc-pCVTZ level of theory predicts that the unpaired electron is primarily located at C 1 .On the basis of bond lengths obtained at the same level of theory, the valence structure of Another relatively high-energy cyclic isomer of MgC 4 H is 1λ 2 -magnesacyclopent-2-ene-4-yne-2-yl (6), which is 216 kJ mol −1 higher in energy than 1.This molecule has a fivemembered ring containing four carbon atoms and one magnesium atom.The magnesium atom is in the same plane as isomer 4 with a C 3 C 4 Mg bond angle of 104.56°.The molecular symmetry of 6 is C s and the ground-state electronic state is 2 A′ with the electronic configuration (1− 6A′) 2 (1A″) 2 (7−12A′) 2 (2A″) 2 (13−15A′) 2 (3A″) 2 (16A′) 1 .The spin distribution calculation at the ROCCSD(T)/cc-pCVTZ level predicts that the unpaired electron is primarily located on C 3 .The optimized geometry shown in Figure 1, C , and C 3 −C 4 (1.263Å), exhibits a partial double bond, a single bond, and an intermediate between a triple and double bond, respectively.The quartet state geometry is unstable with respect to the isomerization process and converted to isomer 4.

WBIs.
The WBIs of the first seven low-lying isomers have been calculated at the ωB97XD/6-311G++(2d,2p) level of theory and are listed in Table 3. WBIs are the electronic parameters that measure the average number of electron pairs shared by two atoms and indicate their bond strength. 77  The Journal of Physical Chemistry A interaction between them is electrostatic, but C 1 −Mg (0.43) and C 4 −Mg (0.31) imply single-bond character.

Topological Analysis.
The electron localization function (ELF) analysis has been carried out for the first seven low-lying isomers to measure the extent of electron delocalization.The color-filled ELF plots for isomers 1 to 7 are shown in Figure 2. The electron densities are represented within the range of 0 to 1, where 0 signifies a poor localization of electron cloud and 1 signifies the highest density of the electron cloud.Due to the more electropositive nature of the magnesium atom compared to carbon, the electron density has shifted toward the carbon atom for each isomer (1 to 7).For example, in isomer 1, the ELF value for C−C and C−H bond is ∼1, which indicates strong electron localization between these bonds, whereas the low ELF value (0.099) between Mg and C signifies poor localization of electrons on the magnesium atom.
The topological parameters such as the Hamiltonian kinetic energy K(r c ), ρ(r c ), Laplacian electron density [∇ 2 ρ(r c )], Lagrangian kinetic energy G(r c ), potential energy density V(r c ), energy density E(r c ) or H(r c ), ELF, G(r c )/V(r c ), and kinetic energy per electron G(r c )/ ρ(r c ) at the (3, −1) bond critical points (BCPs) obtained from the ωB97XD/6-311+ +G(2d,2p) level of theory are listed in Table 4. Out of these, Laplacian electron density (∇ 2 ρ) is an important parameter to characterize a chemical bond.According to Bader's theory, 78,79 interatomic states can be classified based on the magnitude of the Laplacian of the electron density, represented by |V(r c )|. G(r c ) is a positive quantity, whereas V(r c ) is a negative quantity.If |V(r c )| > 2G(r c ), then the interaction between two atoms is covalent in nature, |V(r c )| < G(r c ) represents electrostatic interaction, and G(r c ) < |V(r c )|< 2G(r c ) implies a partially covalent interaction.Similarly, the ratio of −G(r c )/ V(r c ) signifies the bonding interaction.If this ratio is greater than 1, then the nature of the interaction is purely noncovalent.From Table 4, the −G(r c )/V(r c ) ratio for Mg−C and Mg−H bonds in each isomer is ∼1.This infers noncovalent or electrostatic interaction between the Mg and C or H atoms for all isomers between 1 and 7. |V(r c )| and G(r c ) values for these bonds also support this observation.All C−C and C−H bonds are covalent in nature; however, C−H bonds are more covalent than C−C bonds.The BCPs and ring critical points have also been calculated at the same level of theory and are shown in Figure S2.
Table 4. Electron Density Descriptors (in a.u.) at the (3, −1) BCPs Obtained from the ωB97XD/6-311++G(2d,2p) Level for First Seven Low-Lying MgC 4 H Isomers The Journal of Physical Chemistry A 3.4.Spectroscopic Data.The spectroscopic parameters are the main key evidence to identify the molecules in the laboratory and consequently in the ISM.In 2019, Cernicharo et al. have identified isomer 1 of MgC 4 H in IRC+10216 and observed the rotational constant value (B 0 ) as 1381.512MHz. 45In 2008, Maier's group observed the electronic transitions of MgC 4 H by using high-resolution optical spectroscopy and obtained a rotational constant value of B 0 = 1384.7 ± 6 MHz. 49,50Later on, in 2010, Forthomme et al. observed the same electronic transitions of MgC 4 H and provided a much accurate value for the rotational constant B 0 = 1380.9± 0.2 MHz. 51Several theoretical investigations on MgC 4 H have already been done by research groups using various quantum chemical calculations. 49,51,52 From the rotational constant value of 2, one could infer that this isomer is a prolate type of molecule.
3.5.Rearrangement Scheme.A thermodynamically favorable rearrangement scheme has been postulated for the formation of low-lying isomers (1 and 2) from higher-energy isomers at B3LYP/6-311G++(2d,2p).For better refinement in the relative energies, the single-point energy has been calculated at the CCSD(T)/cc-pVTZ level of theory.The activation energy barriers for the isomerization process are relatively lower than the B3LYP results.The minimum energy pathways are verified through IRC calculation at the B3LYP/6-311G++(2d,2p) level.A schematic outline of the isomerization pathways of isomers 6 to 5, 5 to 1, 6 to 4, 4 to 2, and 3 to 2 is shown in Figure 3.
Isomer 6 has a strained three-membered ring, an easy C−C bond breaking leads to the lower-energy isomers.The isomerization of 6 can proceed through two different pathways: (i) the C−Mg bond breaking between the terminal carbon adjacent to carbon having hydrogen and Mg of 6 forms 5.This rearrangement goes through TS1 with a very low activation energy barrier (E a = 2 kJ mol −1 ).One imaginary frequency (ν i ) at 111.08i cm −1 implies the exact vibration of this interconversion.Again, the lowest-energy isomer (1) can be formed by a 1,2-H shifting reaction from 5 through TS2 (E a = 28 kJ mol −1 ; ν i = 912.27icm −1 ).(ii) Newly formed C−Mg bond in 6 can lead to the formation of isomer 4 through TS3 (E a = 17 kJ mol −1 ; ν i = 460.41icm −1 ).From 4, C−C single bond breaking takes place for the formation of 2. Relatively higher activation energy (E a = 101 kJ mol −1 ) is required for this rearrangement through TS4 (ν i = 462.25icm −1 ).Another isomerization can take place from isomer 3 to 2 through TS5 (E a = 56 kJ mol −1 ; ν i = 109.22icm −1 ).The imaginary frequency at 109.22 cm −1 corresponds to the ring-closing reaction.
3.6.Other Higher Energy Isomers of MgC 4 H.Out of the 28 stationary points of MgC 4 H isomers studied in this work, the first 15 isomers are minimum energy isomers and the rest of them are either transition states (having one imaginary frequency) or higher-order saddle points (having more than one imaginary frequencies).From isomers 8 to 15, geometry optimization and frequency calculations have been performed at the UωB97XD/6-311 G++(2d,2p) level of theory.The minimum energy structures are shown in Figure 4, and the transition states are listed in Figure 5. Isomers 12 (303 kJ mol −1 above 1) and 13 (312 kJ mol −1 above 1) are linear structures with dipole moments of 4.73 and 1.12 D, respectively.

CONCLUSIONS
In summary, a total of 28 stationary points of MgC 4 H have been identified using DFT and CC methods.For the first seven low-lying isomers, the relative energies have also been computed at the ROCCSD(T)/cc-pCVTZ level of theory in both their doublet and quartet electronic states.The most stable isomer among them turns out to be isomer 1 in the doublet electronic state.Within the quartet electronic states, isomer 4 was identified as the most stable isomer.Isomers 1, 3, and 7 are linear molecules, and among them, isomer 7 is the most polar isomer (5.53 D).However, it lies in the high-energy region (244 kJ mol −1 higher in energy than 1 calculated at the ROCCSD(T)/cc-pCVTZ level of theory).Among the first three low-lying MgC 4 H isomers, 2 is more polar (cyclic isomer, 2.54 D) and lies 146 kJ mol −1 higher in energy than 1.The calculated rotational constant value of isomer 1 has good agreement with the experimental value (percentage error ≃0.78).Furthermore, CASPT2 calculations have been performed for a few isomers exhibiting multireference characteristics.Isomer 2 would be a promising candidate to be detected in the laboratory and consequently in the ISM.Theoretical spectroscopic parameters collected in this study may aid radioastronomers, laboratory molecular spectroscopists, and synthetic organic chemists to detect these isomers in the near future.
Optimized geometries of the first seven low-lying isomers at their doublet and quartet electronic states in Cartesian coordinates (in Å) obtained at the ROCCSD(T)/ccpCVTZ level of theory; optimized geometries of higher energy isomers at their doublet and quartet electronic states in Cartesian coordinates (in Å) obtained at the B97XD/6-311++G(2d,2p) level of theory; optimized geometries of higher energy isomers at their doublet and quartet electronic states in Cartesian coordinates obtained at the B97XD/6-311++G(2d,2p) level of theory; relative ZPCE, dipole moments, relative zero-point corrected Gibb's free energy, number of imaginary frequencies, and < S2 > of UHF wave function of MgC4H isomers of 1-28 in their doublet ground electronic states calculated at the UB97XD/6-311++G(2d,2p) level of theory; isomers 1-7 of MgC4H The Journal of Physical Chemistry A in their quartet ground electronic states; molecular graph representation of first seven low-lying isomers of MgC4H in their doublet ground electronic states calculated at the ωB97XD /6-311G++(2d,2p) level of theory; higher-order saddle points of MgC4H in their doublet ground electronic states; energy evolution of isomer 1; energy evolution of isomers 2 and 3; energy evolution of isomers 4 and 5; and energy evolution of isomer 6 (PDF) ■
based on single-point energy calculation at the CCSD(T)-F12/cc-pVTZ-F12 level of theory.b

Figure 2 .
Figure 2. Color-filled ELF plots of the first seven low-lying isomers of MgC 4 H in their doublet ground electronic states calculated at the ωB97XD/6-311G++(2d,2p) level of theory.

Figure 3 .
Figure 3. Plausible rearrangement schemes and PES for the formation of low-lying isomers from higher-energy isomers calculated at the CCSD(T)/cc-pVTZ level of theory.
4 has one C−C partial triple bond (C 3 −C 4 ; 1.255 Å), one C−C single bond (C 2 −C 3 ; 1.469 Å), one C−C partial double bond (C 1 − C 2 ; 1.356 Å), two magnesium−carbon bonds (Mg−C 1 2.087 Å and Mg−C 4 2.062 Å), and one weakly attached Mg−C bond (Mg−C 3 ; 2.166 Å).The dipole moment of 4 is 4.88 D at the ROCCSD(T)/cc-pCVTZ level of theory.Therefore, the chances of identifying this molecule in the ISM as well as in the laboratory are high.The quartet electronic state of 4 ( 4 A′) is 173 kJ mol −1 above the doublet 4 and the most stable (18 kJ mol −1 lower in energy than quartet 1) quartet state geometry on MgC 4 H PES. The overall molecular symmetry remains the same in both the electronic states.The Mg−C bond is slightly elongated from the doublet state geometry.
In isomer 1, the WBI values for C 1 −C 2 , C 2 −C 3 , and C 3 −C 4 (atom numbers as indicated in Figure 1) are 2.72, 1.19, and 2.73, respectively, indicating resonance stabilization with alternate triple bonds along the linear molecule.For isomers 2 and 4, the WBI values indicate similar interaction between magnesium and carbon atoms (C 1 −Mg and C 2 −Mg), whereas the WBI value for C 3 −Mg (0.07) of isomer 4 indicates that the

Table 2 .
Inertial Axis Dipole Moment Components, Absolute Dipole Moments (in Debye), Centrifugal Distortion Constants (in MHz), and Rotational Constants (in MHz) of the First Seven Low-Lying MgC 4 H Doublet Isomers Calculated at the ROCCSD(T)/cc-pCVTZ Level of Theory

Table 3 .
WBIs for First Seven Low-Lying Isomers of MgC 4 H Calculated at the ωB97XD

/6-311G++(2d,2p) Level of Theory
In 2019, Cernicharo et al. calculated the rotational constant value for isomer 1 at different levels of theory.They found B 0 = 1357.66MHz at the CCSD(T)/aug-cc-pVTZ level and B 0 = 1376.49MHz at the CCSD(T)-F12/cc-pCVTZ-F12 level of theory.In this work, we performed high-level ab initio calculations to determine the accurate spectroscopic molecular parameters listed in Table 2. Our theoretically calculated rotational constant value (1370.74MHz) at the ROCCSD(T)/cc-pCVTZ level of theory has good agreement with the experimental rotational constant value (percentage error ≃0.78).The calculated equilibrium rotational constants (A e , B e , and C e ) for 2 at the ROCCSD(T)/cc-pCVTZ level of theory are A e = 52023.67MHz, B e = 1683.67MHz, and C e = 1630.89MHz, respectively, whereas CASPT2 calculation of 2 predicts relatively higher rotational constant values (A e = 53285.30MHz, B e = 1737.57MHz, and C e = 1682.70MHz).